Demand systems with heteroscedastic disturbances
Tóm tắt
We address the estimation of singular demand systems with heteroscedastic disturbances. We relax the homoscedasticity assumption and instead assume that the covariance matrix of the errors of the demand system is time varying. In doing so, we consider the VECH and BEKK parameterizations of the variance model. We analytically prove the invariance of the maximum likelihood estimator with respect to the choice of the good deleted from a singular demand system and also prove a number of important practical results regarding how to recover the mean and variance equation parameters (and their standard errors) of the full demand system from those of any subsystem obtained by deleting an arbitrary good.
Tài liệu tham khảo
Banks J, Blundell R, Lewbel A (1997) Quadratic Engel curves and consumer demand. Rev Econ Stat 79:527–539
Barnett WA (1983) New indices of money supply and the flexible Laurent demand system. J Bus Econ Stat 1:7–23
Barnett WA (1985) The minflex Laurent translog flexible functional form. J Econom 30:33–44
Barnett WA (2002) Tastes and technology: curvature is not sufficient for regularity. J Econom 108:199–202
Barnett WA, Jonas A (1983) The Müntz Szatz demand system: an application of a globally well behaved series expansion. Econ Lett 11:337–342
Barnett WA, Lee YW (1985) The global properties of the minflex Laurent, generalized Leontief, and translog flexible functional forms. Econometrica 53:1421–1437
Barnett WA, Serletis A (2008) Consumer preferences and demand systems. J Econom 147:210–224
Barnett WA, Serletis A (2009) Measuring consumer preferences and estimating demand systems. In: Slottje D (ed) Quantifying consumer preferences. Contributions to economic analysis. Bingley, Emerald, pp 1–35
Barnett WA, Liu J, Mattson RS, van den Noort J (2013) The new CFS Divisia monetary aggregates: design, construction, and data sources. Open Econ Rev 24:101–124
Barten AP (1969) Maximum likelihood estimation of a complete system of demand equations. Eur Econ Rev 1:7–73
Berndt ER, Savin NE (1975) Estimation and hypothesis testing in singular equation systems with autoregressive disturbances. Econometrica 43:937–957
Bewley R (1986) Allocation models: specification, estimation and applications. Ballinger, Cambridge
Bollerslev T, Engle RF, Wooldridge J (1988) A capital asset pricing model with time varying covariances. J Polit Econ 96:143–172
Blundell R (1988) Consumer behaviour: theory and empirical evidence—a survey. Econ J 98:16–65
Brown JAC, Deaton AS (1972) Models of consumer behaviour: a survey. Econ J 82:1145–236
Christensen LR, Jorgenson DW, Lau LJ (1975) Transcendental logarithmic utility functions. Am Econ Rev 65:367–383
Deaton AS, Muellbauer JN (1980) An almost ideal demand system. Am Econ Rev 70:312–326
Diewert WE (1971) An application of the Shephard duality theorem: a generalized Leontief production function. J Polit Econ 79:481–507
Diewert WE (1973) Functional forms for profit and transformation functions. J Econ Theory 6:284–316
Diewert WE, Wales TJ (1988) Normalized quadratic systems of consumer demand functions. J Bus Econ Stat 6:303–312
Engle RF, Kroner KF (1995) Multivariate simultaneous generalized ARCH. Econom Theory 11:122–150
Gallant AR (1981) On the bias of flexible functional forms and an essentially unbiased form: the Fourier functional form. J Econom 15:211–245
Lewbel A (1997) Consumer demand systems and household equivalence scales. In: Pesaran MH, Schmidt P (eds) Handbook of applied econometrics, vol 2. Blackwell Publishers, Oxford
McLaren KR (1990) A variant on the arguments for the invariance of estimators in a singular system of equations. Econom Rev 9:91–102
Powell A (1969) Aitken estimators as a tool in allocating predetermined aggregates. J Am Stat Assoc 64:913–922
Serletis A, Isakin M (2017) Stochastic volatility demand systems. Econom Rev 36:1111–1122